Question

the difference of 2 positive numbers is 3 and the sum of their squares is 225. what are the numbers.

Answer 1

Answer:

let the first no. be X

then the second no be X+3

a/q

X²+(X+3)²=225

X²+X²+6X+9=225

2X²+6x-216=0

2(X²+3X-108) =0

X²+3X-108=0

X²+12X-9X-108=0

X(X+12)-9(X+12)=0

(X-9) (X+12) =0

X-9=0

X=9

HENCE THE NO. WILL BE 9 AND 9+3=12

Answer 2

Answer:

If the given numbers are x and y.

Then y = (x-3)

Hence x^2 + (x-3)^2 = 225

=> x^2 + x^2 + 3^2 - 2(x)(3) = 225

=> 2.x^2 -6x + 9 = 225

=> 2.x^2 -6x - 216 = 0

=> 2.x^2 -24x + 18x - 216 = 0

=> 2.x(x -12) + 18(x - 12) = 0

=> (2.x + 18)(x - 12) = 0

So x = 12 since it is given it is positive.

So y = 12-3 = 9.

So The required numbers are 9 and 12.

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